Summary

Biomechanical models are intrinsically limited in explaining the
ontogenetic scaling relationships for prey capture kinematics in aquatic
vertebrates because no data are available on the scaling of intrinsic
contractile properties of the muscles that power feeding. However, functional
insight into scaling relationships is fundamental to our understanding of the
ecology, performance and evolution of animals. In this study, in
vitro contractile properties of three feeding muscles were determined for
a series of different sizes of African air-breathing catfishes (Clarias
gariepinus). These muscles were the mouth closer musculus adductor
mandibulae A2A3′, the mouth opener m. protractor hyoidei and the
hypaxial muscles responsible for pectoral girdle retraction. Tetanus and
twitch activation rise times increased significantly with size, while latency
time was size independent. In accordance with the decrease in feeding velocity
with increasing size, the cycle frequency for maximal power output of the
protractor hyoidei and the adductor mandibulae showed a negative scaling
relationship. Theoretical modelling predicts a scaling relationship for in
vivo muscle function during which these muscles always produced at least
80% of their maximal in vitro power. These findings suggest that the
contractile properties of these feeding muscles are fine-tuned to the changes
in biomechanical constraints of movement of the feeding apparatus during
ontogeny. However, each muscle appears to have a unique set of contractile
properties. The hypaxials, the most important muscle for powering suction
feeding in clariid catfish, differed from the other muscles by generating
higher maximal stress and mass-specific power output with increased size,
whilst the optimum cycle frequency for maximal power output only decreased
significantly with size in the larger adults (cranial lengths greater than 60
mm).

Introduction

Increases in body size during the lifetime of animals have important
implications for the mechanics of their musculo-skeletal system
(Hill, 1950; Schmidt-Nielsen,
1984; Biewener, 2005). When
animals grow, their increased body size will generally impose different
demands upon their morphology, behaviour and/or physiology. Because it is
crucial to know how animals deal with the consequences of changes in size,
studies of scaling relationships are fundamental to our understanding of the
ecology, performance and evolution of animals
(Herrel and Gibb, 2006).

One of the consequences of scaling is that larger aquatic suction-feeding
vertebrates need a longer time to carry out a similar movement of their
cranial system during prey capture (e.g. opening of the mouth or expansion of
buccal cavity by the hyoid) compared with smaller animals of the same species
(Richard and Wainwright, 1995;
Reilly, 1995;
Cook, 1996;
Hernandez, 2000;
Wainwright and Shaw, 1999;
Robinson and Motta, 2002;
Deban and O'Reilly, 2005;
Van Wassenbergh et al.,
2005a). A recent theoretical model
(Van Wassenbergh et al.,
2005a) calculated that for a 10-fold, isometric increase in size,
the time needed to complete a rapid, size-proportional expansion of the
bucco-pharyngeal cavity (which induces suction) increases by a factor of 4.64
[duration of kinematic events scale with length (L)0.66].
In turn, as the time needed to draw prey towards and into the mouth cavity and
the maximal distance from which prey can be caught depend on head size as well
as the speed of feeding movements, these scaling relationships have important
implications for the animal's success in capturing prey
(Van Wassenbergh et al.,
2006).

If the duration of head expansion is assumed to be size independent, the
model (Van Wassenbergh et al.,
2005a) predicts that the hydrodynamic resistance to expand the
bucco-pharyngeal cavity will cause an increase in the required power by
L5 (pressure ∼ L2 × surface
area ∼ L2 × linear velocity of expansion ∼
L1). This size-dependant resistance is primarily dictated
by the forces needed to move head parts in the identical time frames against
the pressure gradient between the inside and the outside of the buccal cavity.
However, similar to most other explosive movements – for example
fast-starts for escaping predators
(Wakeling and Johnston, 1998)–
suction-feeding performance is most probably limited by the maximally
available muscle power (Aerts et al.,
1987; Carroll et al.,
2004; Carroll and Wainwright et al., 2006). The underlying
assumption of the model (Van Wassenbergh
et al., 2005a) is that power output of the muscles that generate
suction is directly proportional to the total mass of these muscles, and is
hence proportional to L3 (as that force is proportional to
muscle cross-section, and contraction speed is proportional to fibre length).
As a consequence of this mismatch between required and available power,
isometrically growing animals must inevitably become slower in suction feeding
during ontogeny.

As isometry also implies size-independent muscle strain (change in length
divided by initial length), the slowing of suction feeding during ontogeny
means that the relative speed of muscle contraction (muscle lengths per
second) should decrease with size. This could have important consequences for
the contractile physiology of the muscles powering feeding. It has been shown
that in an ontogenetic series of aquatic animals, in vitro
contractile properties of fast and slow muscles used in locomotion alter
roughly in accordance with the speed of movement displayed in vivo
(Anderson and Johnston, 1992;
Altringham et al., 1996;
James and Johnston, 1998;
James et al., 1998) (but see
Curtin and Woledge, 1988).
However, to our knowledge, no data on the scaling of contractile properties of
the fast-fibred muscles used for capturing prey are available in the
literature. It is therefore unknown how animals precisely cope with the
different dynamical environments imposed by the effects of scaling on the
mechanics of the feeding system.

In the current study, we present the first data on scaling relationships of
the contractile properties of muscles directly used for capturing prey. We
analysed the contractile physiology of three muscles that are very important
for powering prey capture in the African catfish Clarias gariepinus
(Fig. 1), and presumably also
for fish in general (e.g. Lauder,
1985): the hypaxial muscles, the protractor hyoidei and the
adductor mandibulae A2A3′. By comparing theoretical scaling predictions
of maximal speed of prey capture in catfish
(Van Wassenbergh et al.,
2005a) with in vitro contractile properties of the three
feeding muscles from a range of catfish of different body sizes, we can test
whether or how the contractile properties of these muscles are adjusted as a
function of the biomechanical constraints of feeding causing the speed of
muscle contraction to reduce during ontogeny.

Materials and methods

Animals

Sixteen Clarias gariepinus (Burchell 1822) individuals between
14.4 and 205.4 mm in cranial length were used in this study. As the cranial
length (defined as the distance between the rostral tip of the premaxilla and
the caudal tip of the occipital process) can be measured more precisely and
excludes variability in the length of body and tail, we used this metric to
quantify size. Body mass varied from 1.83 g to 4770 g in this series of
African catfish. Awaiting the experiments, all animals were kept in the same
room at 22°C, each in a separate aquarium of which the dimensions were
roughly proportional to the size of the fish. Each fish was killed by
concussion of the brain by striking of the cranium, followed by destruction of
the brain and transection of the spinal cord in accordance with the UK Home
Office Animals (Scientific Procedures) Act 1986. The individuals used were
either aquarium-raised specimens obtained from the Laboratory for Ecology and
Aquaculture (Catholic University of Leuven, Belgium) or specimens obtained
from aquaculture facilities (Fleuren & Nooijen BV, Someren, The
Netherlands). However, catfish from both origins did not show different growth
patterns of the feeding apparatus (Herrel
et al., 2005). This species was chosen because scaling
relationships of morphology (Herrel et
al., 2005) and prey capture kinematics
(Van Wassenbergh et al.,
2005a), as well as a more detailed study on functioning of the
cranial system (Van Wassenbergh et al.,
2005b), are available in the literature and can thus be used to
interpret the results. Also, individuals of different sizes were readily
available.

Lateral view of the head of a juvenile Clarias gariepinus of 125.5
mm standard length [after Adriaens et al.
(Adriaens et al., 2001)].
Indicated are the three muscles used in this study. Scale bar, 5 mm.

Muscle preparations

Three muscles were studied (Fig.
1): (1) the hypaxials (abbreviated m-hyp), the most important
muscle for powering head expansion in clariid catfish; (2) the musculus
protractor hyoidei (abbreviated m-pr-h), functioning as a mouth opener in
C. gariepinus (see Van
Wassenbergh et al., 2005b) and (3) the musculus adductor
mandibulae A2A3′ (abbreviated m-a-m), the largest part of the jaw
adductor muscle complex, responsible for closing the mouth rapidly and
exerting bite force onto prey. From this point on, the abbreviations m-hyp,
m-pr-h and m-a-m will be used to refer to these muscles (see also
Fig. 1). The m-pr-h and m-a-m
of a single side were dissected as a whole, leaving it attached to the part of
the bones that serve as the muscle's origin and attachment. The anterior part
of the m-hyp was dissected out. Next, the muscle preparations were transferred
to a Ringer solution maintained at 4°C. The composition of the Ringer
solution used in the present study is identical to the one used for
Cyprinus carpio (Wakeling and
Johnston, 1999). Small bundles of m-hyp muscle fibres were
dissected from the anterior part of the m-hyp using a dissecting stereoscope.
The resulting m-hyp muscle preparations always originated from approximately
one-third of the animal's cranial length posterior to the medial attachment
with the cleithrum.

The bone at either end of the muscle preparation was clamped via
crocodile clips to a strain gauge (UF1; Pioden Controls Ltd, Inverness, UK) at
one end and a motor arm (V201; Ling Dynamics Systems, Herts, UK) attached to
an LVDT (Linear Variable Displacement Transformer; DFG 5.0; Solartron
Metrology, Leicester, UK) at the other. Meanwhile, the preparation was placed
into a flow-through chamber of oxygenated Ringer solution that was kept
between 26.8 and 27.2°C (close to the optimum temperature used for
breeding C. gariepinus) (Hossain
et al., 1999). For the m-hyp bundles, aluminium foil T-shaped
clips were folded over the myoseptum at both ends of the muscle fibre bundle,
and these foil clips were clamped into the crocodile clips, as detailed above.
Electrical stimulation was delivered via a pair of platinum
electrodes running parallel to the muscle preparation.

Isometric contractile properties

The length of the preparation was adjusted to give maximal twitch force,
thereby putting the sarcomeres close to their optimal length for maximal force
production (Rome and Sosnicki,
1991). The length at which the muscle produced maximal force
(L0) was measured using digital calipers (±0.1 mm).
Stimulation amplitude and pulse width were also adjusted to maximize twitch
force. A pulse width of 1.5 ms was used. Stimulation frequency was adjusted to
maximize tetanus height. In order to allow accurate quantification of rise
times, tetanus stimulations were sustained for 150 ms for the m-hyp and 300 ms
for the m-pr-h and m-a-m. A recovery time of 5 min was allowed between each
tetanus. Latency (time between the onset of stimulation and the start of force
production), time to peak twitch force and time to 50% of peak tetanus force
were measured to indicate the rate of force increase.

In vitro power output

The work loop technique (Josephson,
1985) was used to measure power output of the muscles subjected to
sinusoidal cycles of lengthening and shortening about L0.
A sinusoidal strain waveform with a total strain of 10% of
L0 (±5%) was imposed during the experiments, as
this approximates the in vivo shortening pattern measured for the
m-pr-h by high-speed X-ray video of C. gariepinus during prey capture
(Van Wassenbergh et al.,
2005b). Using the model of Van Wassenbergh et al.
(Van Wassenbergh et al.,
2005c), we calculated that a 10% strain in the m-a-m corresponds
to the situation in which the mouth is closed from a gape angle of 47°,
which is relatively high, but perfectly feasible for this species. Because no
data are available on strain amplitude of the m-hyp during feeding, we used
the same shortening–lengthening regime as for the other two muscles to
enable direct comparison (10% sinusoidal strain).

Muscles were subjected to sets of four cycles of active work loops, of
which the second cycle was selected for further analyses. Note that relatively
small differences were observed between the consecutive cycles: maximal net
contractile power for the second cycle in a random sample of 10 sequences from
the m-hyp, m-pr-h and m-a-m are 92±5%, 97±6% and 103±16%
(mean ± s.d.), respectively, of the first cycle. A recovery time of 5
min was allowed between each work loop run. The net power per cycle, however,
is a complex function of strain, cycle frequency, number and timing of stimuli
(Altringham and Johnston,
1990). Therefore, in order to analyze the optimum cycle frequency
for producing power, each preparation was subjected to at least six different
cycle frequencies. The number of stimuli per cycle and the stimulation phase
(timing of stimulation) was varied at each cycle frequency to maximize power
output. To monitor progressive changes in contractile performance, the
conditions used at the first cycle frequency were repeated after every three
sets of work loops. A loss of about 15% in power output was typically observed
after six consecutive sets of work loops, which is presumably caused by some
fibres becoming inexcitable. Any loss in power output was due to a reduction
in force production during the work loop, rather than a change in work loop
shape. To correct for this deterioration in muscle power output, a linear
interpolation of power loss-percentage as a function of time was used.

At each cycle frequency, the muscle was subjected to a set of four passive
work loops, i.e. without electrical stimulation. These passive force values
(from passive work loops) were subtracted from the corresponding active forces
(from any active work loops at the same cycle frequency) to give the active
contractile force (Fig. 2A,C).
Instantaneous power was calculated as the product of this contractile force
and the velocity of movement. Average power in each movement cycle was
calculated as the instantaneous contractile power averaged over the entire
movement cycle. All power outputs subsequently reported are those averaged
across a full work loop cycle. A zero phase-shift, fourth-order low-pass
Butterworth filtering of the measured force and length data was applied to
reduce noise in the work loops (Fig.
2A). A standard cut-off frequency of 60 times the sampling
frequency was used, followed by a graphical check and (if necessary) an
adjustment of the cut-off frequency to achieve adequate filtering.

After the experiments, muscle tissue was dissected from the preparation and
muscle mass was determined (±0.01 mg). Any dead fibres were removed
from the outer edges of the muscle to ensure that any muscle fibres damaged
during dissection were removed. Cross-sectional area was calculated by
dividing muscle volume (assuming a density of 1060 kg m–3)
(Mendez and Keys, 1960) by
L0. Maximal isometric stress was calculated by dividing
maximal force by cross-sectional area. Maximal normalized power output was
calculated relative to wet mass to take account of differences in size of
muscle preparations. The proportion of connective tissue within the muscles is
assumed not to change with body size or differ between muscles used in this
study. However, as connective tissue has relatively low density and is a small
proportion of the muscle volume, this assumption seems justified since
potential differences will probably have a small effect on muscle density.

Example of a work loop (A) generated during 8 Hz sinusoidal length changes
(strain of 10%) for the musculus protractor hyoidei (m-pr-h) of an 80.1 mm
cranial length C. gariepinus, with (B) the corresponding
instantaneous relative speed, (C) force per muscle cross-sectional area and
(D) muscle-mass-specific power output. In A, raw data points are shown as well
as the work loop curve after Butterworth filtering. The force produced by only
the actively contracting components of the muscle was calculated by
subtracting the force measured without stimulation (passive work loop) from
the force with stimulation (active work loop).

Values of maximal force and power were discarded for any muscle preparation
that failed to generate above 20 kN m–2 during tetanic
stimulation. This occurred in seven out of 48 muscles that were analyzed,
without displaying a correlation with the size of the animals studied (m-hyp,
16.0, 205.4 mm; m-pr-h, 16.0 mm; m-a-m, 16.0, 21.0, 190.0, 205.4 mm cranial
length). It is assumed that these discarded preparations had a large fraction
of the muscle fibres that had died between the time of sacrificing the animal
and placing the dissected muscle into the Ringer solution. The data for these
preparations clearly fell below the lower 95% confidence interval of the rest
of the data, which further reassured us that the results from these
preparations were not representative of the rest of the collected data. Our
impression was also that any muscle preparation that produced less than 20 kN
m–2 stress underwent rapid deterioration in contractile
performance.

It should be noted that cyclic length changes imposed on the muscle
preparations, as performed in the present study, might not always be the most
ideal condition for mimicking the in vivo behaviour of feeding
muscles. Nevertheless, the m-a-m will inevitably be stretched prior to mouth
closing, and consequently has a clear eccentric phase and an overall strain
pattern approximately similar to the sinusoidal waveform of
lengthening–shortening imposed in the presented in vitro
experiments. A short eccentric phase of relatively small amplitude and an
approximately overall sinusoidal strain pattern can also be recognized for the
m-pr-h during prey capture in C. gariepinus
(Van Wassenbergh et al.,
2005b). However, for the post-cranial muscles used for pectoral
girdle retraction or neurocranial elevation (e.g. m-hyp), measuring power
output when activation starts during lengthening may not be fully
representative of the in vivo situation in which activation of the
muscles is normally followed by a concentric contraction
(Carroll and Wainwright, 2006;
Coughlin and Carroll, 2006).
However, given the purpose of the present study, i.e. analyzing scaling
effects on contractile properties, it is very unlikely that this could have
influenced the observed scaling relationships (more specifically, the slopes
of log–log regressions). Furthermore, using also the work loop technique
for the m-hyp has the important advantage of enabling comparison between the
different feeding muscles and comparison with most of the data available in
the literature on other types of muscle (e.g. muscles used for
locomotion).

Relationships between cycle frequency and power output

The maximized contractile power outputs of at least six work loops of
differing cycle frequency were plotted against cycle frequency. A third-order
polynomial fit was used to determine the cycle frequency for maximal power
output. Power output values were then expressed as a percentage of maximum
power, and ranges were determined for cycle frequencies yielding at least 90%,
80% and 70% of this maximum.

Scaling relationships of the cycle frequency for maximal power output were
compared to a model prediction of scaling relationships for in-vivo
shortening speed of the m-pr-h and m-a-m in C. gariepinus during prey
capture. The inverse dynamical model by Van Wassenbergh et al.
(Van Wassenbergh et al.,
2005a) accounts for the allometry in muscle mass in this species
(assumed to influence mass-specific power output) as measured by Herrel et al.
(Herrel et al., 2005) and
predicts that movement durations increase with the animal's head length
(L) by L0.53. High-speed X-ray video data on
shortening speeds of the m-pr-h and m-a-m
(Van Wassenbergh et al.,
2005b) were used to determine the intercept for the scaling
regressions. To do so, for each of the three individuals studied by Van
Wassenbergh et al. (Van Wassenbergh et
al., 2005b), five feeding sequences in which the strain was
closest to 10% were selected. The reciprocal of twice the average duration of
the shortening phase was used as a measure for sinusoidal strain cycle
frequency. Finally, scaling regressions were plotted through the point in
which cranial length and frequency were averaged for the three
individuals.

Statistics

All data were log10 transformed (one data point for each
individual) and were plotted against the log10 of cranial length.
Next, least-squares linear regressions were performed on these data. As the
measured physiological variables (dependent data) are likely to have a much
greater error than measurements of cranial length (independent data),
least-squares regressions are appropriate in this case
(Sokal and Rohlf, 1995). The
slopes of these linear regressions with 95% confidence limits were determined
in order to evaluate changes in contractile properties of the muscles in
relation to changes in body size. Note that a near-isometrical relationship
exists between cranial length and body mass (log–log regression slope of
2.96, r2=0.99), implying identical scaling results if the
cube root of body mass would have been used to quantify size.

Each linear regression was tested for statistical significance by an
analysis of variance (ANOVA). To compare the observed regression slopes
against model predictions, the significance of the regressions after rotating
the frame of reference of the data with respect to the predicted slope, which
becomes parallel to the new x-axis, was tested by ANOVA. Differences
between the muscles in the scaling regression slopes for a given variable were
tested (F-test of interactions by covariates) using cranial length as
a covariate in an analysis of covariance (ANCOVA). Only if these slopes did
not differ significantly (P>0.05) could differences in the
intercept for the different muscles be evaluated statistically without
violating the ANCOVA assumption of parallelism.

Results

Latency and rise times of isometric contractions

No significant scaling relationships were observed in the time between the
onset of stimulation and muscle force output
(Fig. 3;
Table 1). Furthermore, this
latency time did not differ between the three muscles (ANCOVA,
F2,41=1.1, P=0.34). The mean latency of the
entire data set was 1.8±0.6 ms (mean ± s.d.).

The times to peak twitch force increased significantly with size for each
of the three muscles (Fig. 3;
Table 1). Values approximately
doubled from the smallest to the largest fish used in this study. The scaling
relationships (regression slopes) for this variable did not differ
significantly between the muscles (ANCOVA, F2,41=2.5,
P=0.09). However, after eliminating size effects, twitch rise times
differed significantly between the muscles (ANCOVA,
F2,43=8.5, P=0.0008). A pairwise comparison
showed that the m-hyp had a significantly shorter twitch rise time compared
with the m-pr-h (ANCOVA, F1,29=6.95, P=0.013)
and, even more pronounced, compared to the m-a-m (ANCOVA,
F1,28=14.7, P=0.0007). The m-pr-h did not differ
significantly with the m-a-m in the time to peak twitch force (ANCOVA,
F1,28=3.4, P=0.08).

The times to half peak tetanus force also increased significantly with size
for the m-hyp and m-pr-h (Fig.
3; Table 1) but not
for the m-a-m (P=0.057; Table
1). Similar to the twitch rise times, significant differences
between the muscles were observed for the rise times during tetanus activation
(ANCOVA, F2,43=14.8, P<0.0001). Also, the
scaling relationships (regression slopes) were not statistically different
between the muscles (ANCOVA, F2,41=0.2, P=0.8).
Again, the m-hyp had the fastest tetanus rise time. The m-pr-h was
intermediate between the m-hyp and the m-a-m and differed significantly from
both muscles (ANCOVA, F1,29=14.2, P=0.0008;
F1,28=4.45, P=0.044, respectively).

Maximal isometric stress

Maximal force per cross-sectional area of the muscle increased continuously
with size for the m-hyp (Fig.
4A; Table 1) in
both twitch and tetanus responses. Although the same overall trend can be
observed for the m-pr-h (Fig.
4B; Table 1), no
significant scaling relationship could be demonstrated if the two smallest
individuals in the study were excluded from the regression analysis. In
contrast to the m-hyp, the maximal isometric force of the m-a-m did not
increase significantly during ontogeny
(Fig. 4C;
Table 1).

(A–C) Log–log plots of cycle frequency for maximal muscle power
output versus cranial length. Observations of in vivo cycle
frequency for three individuals inferred from high-speed X-ray videos are also
shown (black circles). The scaling relationship predicted by inverse dynamic
suction modelling (speed scales with L–0.533)
(Van Wassenbergh et al.,
2005a) is also illustrated (black line). Note the apparent
breakpoint in the scaling relationship for the m-hyp (A) in which only fish
greater than 60 mm show a significantly negative slope in this scaling
relationship. Since no data on in vivo m-hyp strain during feeding
are available, the intercept of the scaling regression predicted by modelling
could not be determined in A. Table
1 gives additional regression statistics. Abbreviations: m-a-m,
musculus adductor mandibulae A2A3′; m-hyp, hypaxials; m-pr-h, protractor
hyoidei.

Power output–cycle frequency relationships

The cycle frequency for maximal power output was independent of size for
the m-hyp (Fig. 5A;
Table 1) but decreased
significantly during ontogeny for the m-pr-h and the m-a-m
(Fig. 5B,C;
Table 1). As a consequence, the
scaling relationship of optimum shortening velocity for producing power
differed significantly between the muscles used in the present study (ANCOVA,
F2,41, P=0.006). The slopes of the regressions
for the m-pr-h (Fig. 5B) and
the m-a-m (Fig. 5C) did not
differ significantly (ANCOVA, F1,27=0.28, P=0.6).
The cycle frequency for generation of maximal power output of the m-a-m was,
irrespective of size, significantly lower than that measured for the m-pr-h
(ANCOVA, F1,28=15.3, P=0.0005).

However, a closer inspection of the power-output–cycle frequency
relationship for the m-hyp (Fig.
5A) suggested the presence of a breakpoint at a cranial length of∼
60 mm. For fish with cranial lengths greater than 60 mm, the cycle
frequency for maximal power output decreases significantly (P=0.0005)
with a slope of –0.54±0.10 (N=10,
r2=0.79). Below the breakpoint, this scaling relationship
is size-independent (slope=–0.01±0.17; N=6,
r2=0.00, P=0.98). The approximate position of the
breakpoint was indicated by a sudden increase in r2 at
this point after one-by-one removal of the smallest individuals from the data
set.

The cycle frequency for maximal power output decreased with size
significantly less rapidly than expected on the basis of the model
calculations for the m-pr-h and for the m-hyp of fish smaller than 60 mm in
cranial length (both P<0.0007;
Fig. 5A,B). On the other hand,
no significant differences between model prediction (slope of –0.533)
and the measured slope are observed for the m-a-m (P=0.95) or the
m-hyp of fish greater than 60 mm (P=0.98). This scaling relationship
predicted by modelling stays within the plateau region where 90% and 80% of
the optimum power is produced, respectively, for the m-pr-h and the m-a-m
(Fig. 5B,C).

No significant differences between the scaling slopes of the three muscles
are found if the m-hyp data of only the fish greater than 60 mm are considered
(ANCOVA, F2,35=0.97, P=0.39). However, after
eliminating size effects, cycle frequencies for maximal power output differed
significantly between the muscles (ANCOVA, F2,37=93.3,
P<0.0001). A pairwise comparison showed that the m-hyp had a
significantly higher cycle frequency for maximal power output compared with
the m-pr-h (ANCOVA, F1,23=205.4, P<0.0001). In
turn, the m-pr-h shows a significantly higher cycle frequency for maximal
power output compared with the m-a-m (ANCOVA, F1,23=15.3,
P=0.0005).

Maximal in vitro power output

The scaling relationships of the in vitro maximal mass-specific
power output (Fig. 6) were
similar to the results for maximal tetanus force per cross-sectional area of
the muscle (Fig. 4). Power
output increased significantly during ontogeny for the m-hyp
(Fig. 6A;
Table 1) and also for the
m-pr-h during the juvenile developmental stages
(Fig. 6B). By contrast,
mass-specific power output was independent of size for the m-a-m
(Fig. 6C), and also for the
m-pr-h for C. gariepinus individuals approximately larger than 40 mm
in cranial length (Fig.
6B).

Logically, in order to optimize performance, the contractile properties of
muscles should be tuned to the contractile regime of the muscle. Hill pointed
out that differences in body size between animals cause a strong need for
changes in contractile characteristics to match alterations in functional
demands (Hill, 1950). Relative
speed of limb movement, for example, differs greatly between mouse and horse,
and so does the contractile physiology of their limb muscles
(Medler, 2002).

However, large differences in body size are not only found when comparing
different species but also during ontogeny of animals like C.
gariepinus and many other ectotherms, where length and mass increase
several orders of magnitude. In these animals, the muscular properties must be
fine-tuned during growth in order to reach a situation in which the muscles
can work under their optimal contractile regime. As developmental constraints
are involved in this process, ontogenetic studies are not identical to
interspecific comparisons.

Yet, ontogenetic studies of contractile properties of fish swimming muscles
(Anderson and Johnston, 1992;
James et al., 1998) have shown
that isometric activation times are significantly longer in larger fish, and
the cycle frequency for maximal power output reduced when fish increase in
size (Altringham and Johnston,
1990; Anderson and Johnston,
1992). In the present study, we see a similar trend for the
fast-fibred feeding muscles of C. gariepinus (Figs
3,
5). Especially for the m-pr-h,
the muscle used for opening the mouth, the in vitro observations for
the cycle frequency for maximal power output are, as expected, very close to
the direct in vivo measurements of shortening velocity during prey
capture (Fig. 5B). These
findings suggest that the contractile physiology of the m-pr-h is well-adapted
to produce maximal power during suction feeding. The in vitro power
optimum for the m-a-m, the mouth-closer and biting muscle, appears to be
reached at slightly higher shortening speeds than the ones inferred by
modelling based on high-speed X-ray video data
(Fig. 5C). Nevertheless, both
muscles' scaling relationships of speed versus cranial length
predicted by modelling (Van Wassenbergh et
al., 2005a) fall entirely within the range of 80% of the optimum
power generation for the complete range of sizes used in the present study.
This suggests that the theoretical predictions of scaling of feeding
kinematics are in close accordance with the contractile properties of the
muscles used for powering feeding in the African catfish.

A critical assumption in studies trying to explain the scaling of feeding
kinematics and performance (Van
Wassenbergh et al., 2005a; Van
Wassenbergh et al., 2006) is that the power output of a muscle
scales with the mass of this muscle (i.e. constant muscle-mass-specific
power). Our data show that this holds true for the m-pr-h (excluding the
juveniles smaller than 20 mm cranial length;
Fig. 6B) and the m-a-m
(Fig. 6C). Even if we account
for the slowing down of contraction speed of the muscles with increasing
catfish size, the observed scaling relationships of optimum-power–cycle
frequency (Fig. 5;
Table 1) has very little
influence on this mass-specific power output because of the relatively small
difference from the predicted scaling relationship (angular speed proportional
to cranial length–0.533)
(Van Wassenbergh et al.,
2005a).

Remarkably, the m-hyp shows different scaling relationships from the m-pr-h
or the m-a-m (Table 1). As
maximal stress of the m-hyp increases significantly with size
(Fig. 4A), the intrinsic
properties might still be under development until the late adult stages. A
study of the expression of myosin isoforms could potentially explain this
unexpected result. It should be noted that the power output of this muscle
already reaches approximately the level of the other two muscles (m-pr-h and
m-a-m) at fish with head sizes of 30 mm. The highest values for power output
are also measured for the m-hyp (Fig.
6). Consequently, except for the smaller juveniles, the crucial
role of the m-hyp for generating suction power is well supported by the
physiological data.

Rather unexpectedly, the m-hyp of juveniles and smaller C.
gariepinus adults (cranial length smaller than 60 mm) differs from the
other muscles in its size independence in the cycle frequency for maximal
power output (Fig. 5A). This
scaling relationship changes for the m-hyp of the larger fish, which show the
more general decrease in cycle frequency for maximal power output with
increasing size (see Fig. 5).
Unfortunately, too little is known about the in vivo contractile
behaviour of the m-hyp to explain these results. From a functional point of
view, there is a fundamental difference between the m-hyp and muscles like the
m-pr-h and the m-a-m. While the latter muscles have a clear origin and
insertion, the m-hyp in C. gariepinus and nearly all other fish
continues posterior into the ventral body musculature
(Diogo et al., 2001).
Activation patterns in the epaxials, a muscle similar to the m-hyp in this
respect, are not spatially uniform; muscle activation intensity recorded for
the anterior region of the epaxials is consistently higher than from the more
posterior region in the percomorph fish, Micropterus salmoides
(Thys, 1997). This implies
that patterns of strain and strain rate within muscles like the epaxials and
hypaxials can also be spatially non-uniform. Furthermore, the m-hyp is not
only used for feeding but also contributes to the lateral undulation during
swimming (e.g. Altringham and Ellerby,
1999). The difference in the scaling relationships of the m-hyp
compared with the other muscles may therefore be a result of the dual function
of this muscle and the consequent potentially different developmental
constraints involved.

Small differences in intrinsic contractile properties such as twitch and
tetanus times and maximal shortening velocities
(Fig. 3) do not necessarily
have biological relevance (Caizzo and
Baldwin, 1997; James et al.,
1996). However, the recorded times to peak twitch force and times
to half peak tetanus force (Fig.
3) were significantly correlated with the cycle frequencies for
optimal power output in our data (N=40, r2=0.41
and 0.35, respectively, P<0.0001). As the same differences between
the three muscles (Fig. 1) were
observed in each of these three variables, our data suggest that ontogenetic
changes in relatively simple measurements such as twitch or tetanus rise times
can already be indicative of size-related changes during work-loop
experiments, which more closely reflect the in vivo dynamic
conditions of the muscles.

It should be noted that certain morphological modifications may help reduce
the extent to which the contractile properties need to be adjusted during
ontogeny in order to keep muscles working at the plateau of the
power–speed curve during feeding. The latter can only be accomplished if
the muscle shortening rateΔ
L/(L0Δt) remains constant
for animals of different sizes, with time increment Δt
inevitably increasing with body size due to the biomechanical consequences of
scaling (Hill, 1950;
Van Wassenbergh et al.,
2005a). This can either be done by (1) negative allometric growth
of muscle length L0 or by (2) positive allometry in the
total length change of the muscle ΔL for a given movement. The
first solution seems to occur in the catfish Clarias gariepinus,
where fibre lengths of some cranial muscles show a slight negative allometry
(Herrel et al., 2005) while
the length of the moment arms of the jaw system and the magnitude of excursion
of the cranial elements during feeding scale approximately isometrically
(Van Wassenbergh et al.,
2005a). Note that this means the slope of the scaling model
prediction line may actually be less steep than shown in
Fig. 5, which would result in
the model predictions corresponding even better to the frequencies for optimal
power output measured in vitro.

The second option seems to occur in the sunfishes Lepomis
punctatus and Lepomis macrochirus, for which both the in-levers
and out-levers of the lower jaw scale with positive allometry
(Wainwright and Shaw, 1999).
This means that if the rest of the feeding apparatus grows isometrically, a
given rotation of the lower jaw will cause a relatively larger length change
in the muscles that cause mouth opening and mouth closing. Therefore, similar
to the catfish, a small increase in the strain of the muscle fibresΔ
L/L0 during ontogeny may occur in these
sunfishes, which potentially helps the fish to produce maximal power during
feeding over a wider range of body sizes. Consequently, the speed of
contraction of the muscle fibres will decrease less rapidly with size.
Obviously, only limited changes in muscle strain during ontogeny are possible
due to the force–length relationship of muscle. Therefore, we
hypothesise that the physiological changes manifested in the negative scaling
of the cycle frequency for optimum power output
(Fig. 5) are more important to
maintain optimal power output compared with morphological modifications
increasing ΔL or decreasing L0 in the
course of ontogeny.

Irrespective of scaling relationships, the three muscles analyzed in the
present study differ in several contractile properties. An example of these is
the significantly lower cycle frequency for maximal power output for the m-a-m
compared to the m-pr-h (Fig.
6B,C). Interestingly, this is in accordance with the natural
behaviour of these muscles: the m-pr-h, used for fast mouth opening, generally
shows higher contraction velocities compared with the jaw adductor muscle
(m-a-m) during feeding, and this is reflected in the force–speed
relationship of the muscle. In addition, the latter muscle is also used for
exerting static bite force onto prey
(Herrel et al., 2002). Our
study therefore showed that fast-fibred muscle of the feeding system cannot be
regarded as `similar' with reference to their contractile physiology. Because
the observed differences in in vitro contractile properties between
different muscles matched our expectations based on in vivo
measurements of feeding kinematics (Van
Wassenbergh et al., 2005b), these results suggest that, within a
single species, muscle physiology can be fine-tuned to relatively small
differences in the contractile regime of a muscle. However, as considerably
larger differences between contractile properties of a specific muscle from
small and large catfish were observed, our study particularly emphasises the
importance of the effects of scaling for the mechanics of musculo-skeletal
systems at the level of muscle physiology during ontogeny.

Acknowledgments

Thanks to F. Ollevier, F. Volckaert and E. Holsters for providing us with
the largest individuals used in this study. W. Fleuren is acknowledged for
supplying all other C. gariepinus specimens. Thanks to Mark Bodycote
for technical assistance, and the two anonymous reviewers for their helpful
comments. The authors gratefully acknowledge support of the Special Research
Fund of the University of Antwerp. S.V.W. and A.H. are postdoctoral fellows of
the fund for scientific research – Flanders (FWO-Vl).

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